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Appendix E
GUIDANCE EQUATIONS
E-1/2
Appendix E
GUIDANCE EQUATIONS
L INTRODUCTION
This appendix describes the operational IGS guidance equations.
In general, these equations have been derived in Appendix A and in ref-
erences 1 through 7 listed in Appendix H.
Certain portions of the guidance equations are presented which have
specific application to the GEMINI IGS and have not been derived in the refer-
enced documents. A discussion of the IGS equations as implemented in the
simulation has been included in this appendix to present the simulation oper-
ation in moredetail.
Il. DESCRIPTION OF IGS ASCENT GUIDANCE OPERATION
This section defines the operation of the Ascent Guidance equations dur-
ing launch. Numbers in parentheses refer to areas or blocks in the Ascent
Math Flow Diagrams (Figures E-1A and E-1B). See Table E-I for the definitions
of symbols. The platform is aligned as described in Appendix A. The word
"eontinuously"' when used in the discussion of computer operations means that
the information is updated at approximately 0. 5-sec. intervals.
A. FROM START TO PLATFORM RELEASE
The computer will first be turned to the Ascent mode. All quantities
which require initialization are contained in block A102. Agena ephemeris
data will be inserted into the computer approximately 60 sec.prior to launch.
This information will be continuously updated (A112) and will be used to de-
fine the azimuth orientation of the platform X-axis with respect to East (y) and
the angle between the orbit plane and the launch site (8). The initial conditions
on the spacecraft velocity along platform axis (A117) and the initial platform
roll gimbal angle @y - A116) wiil also be computed continuously.
At approximately 30 sec. prior to launch, the platform will be released
from torquing.* The guidance system is now in the inertial mode.
*As of 28 January 1963, this time — 30 sec. prior to launch — is not definite
and may eventually be "time of engine ignition."
I 9 8 I 7 ih : 6 | 5 4 I 3 2 I 1REVISIONS
sym [enara novice DESCRIPTION pate [ewx] arprovatA RELEASED URfea MALCIraB RELEASE WTTe :
FROMAus A226 & 280SLOW LOOP (2 SAMPLES/ SEC) oe
EROMUEYEC All4 A153PLATFORM COMPUTE
All RELEASED fee SIN #COSACCELEROMETER DI 36 A132 : Oe to,SUBROUTINE ae At = AttAts |
(Fx, Fy, Fe) ANS Ats:0 Al48 | A\54
BoE TO Or. = On Nzo= SIN YeSIMULATION Le2 - Ori + On Na =COS ¥COSO,oes cy Yer = Vw N2r=SIN Od
Allé PH AIS3 pacaraia
Wa =Wae 6Y4=SOn26Q.2O ASCENT Ny = SIN § RteX? +2472 f N 2=COS ho= " Bees ° 2 a =COS*, SING
Te=175 A¥y=AQy=A@y-O INITIALIZATION @n=Cs-X¥+90 R =VRE £ Nes b baK aa -— :
Vir*O Go = 40-0 LC 4A, 4C,4D4E,4F+ ¢ ‘ eg [tse-% To Biase GOStsceeee61-0 LC 4B- COS82COSs |AII7 é A202Uae tc. _—*18,204 GeeCaCO a A155 ASG _ AIST AISBVatVin VyuzO . LC 2\,24,+ SdOe SINS Sake [este -t}* ta-% Dart tant
X= Ko Ko= Vai 2 = cS A =ByAo Y=Vo Le Son Ze2 Ver A\SO§Ww:0 Zo Tus 100 A227Qu =Qo B= Oyn==Vx stiAt -At,=0 Alls x= Yat AN Eee Alél : a
ag: Aso Dw = Dw + Ki (COS*8.)‘COS *8(AL) nw =71.25 "fee. | me |te * tz O@n- 90° Beeogek. cosy (At) le On = OntGn AL Ou=O0
Yun +K’s SIN YA) Vatisny = WaiVycieny = Vi A\S\
TO Veti-n = Vee Vans te
x 102 Ce Vai: Vai 1AaX = X+B X(t)
A106 Z=Z+AZ (tu)
READ TgA\52
A\35 AX=-AnZoVai. = Vai) FadaBt AértAn XoWi = Vy (inn tFy-Sy ALVai = Vein tFe-32At
Ale4 [eeu A\36
| X#X4 (Vat Vari ‘= “PoomAll2 Al25 Ye Y+(WitWeda) : A232
COMPUTE G-R= (G-2)+Abt (Re-W’) tar -Ce Ze Z +(e tVorieahe A Ale7cost COS (9-2), S/IN(D-11) lAQa =i SINS+ SIN 8(K5 HGSIN OKA ney, CALCULATESIN SIN ¥= + SIN COS(O-R) hereeres | een
. a= 3) 1 *Du-1-25 ATR COS Onoesas (+ 6 ta-Ce-ATR Be SET- BY DCS SIN Yn
SIN &=-a,COSL+a,SINL S/N @-S2) ————_ WHEN UP DAG COS Wy
SIN2% COMMAND .cos y+|->p RECEIVED
e AI39 A\68Allo A126 YE-PCOSOn
COMPUTER aaa OP oatRUNNING ON is= y=-GSIN PwDO-05 -
[ee eee. A\66+ On -On + Ou Ab
On=6u+6nu AtWn = Yu t¥n At
Uae
Al46 A169
~Veur-Va" CALCULATEVxup - Xo S¥n=Y¥n At!
; A\47 SOn=On AUAl2e Wat = Weir (Vye=Vr) SOx =On AX!
Vaue = VxCi- 1S t (Vxi- Vx (é-1)) Viz Vel+ (V2/-Vaur):Veue = Vz (t-\)6t (Vzi- Vz(i-)) Vxi = Vi + (Vie -Vaur)
VoveWirtWi- Vv (i-1)) XIOS i
A129 [ease
Tos Ty +50 ASCENTve Tu
| | | |ee a eS Eee Ee Eas
LIST OF MATERIAL OR PARTS LIST
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I 3 I 8 I 7 I 6 T 5 I 4 I 3 I 2 | 1
Figure E-1A. GEMINI Computer Math Flow Diagram Ascent
E-4
1 = _L
A= (an-T)2+(23, VeVe)2I|
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INSIDE x‘ALL DIMENSIONS AND TOLERANCES
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NEW YORK 22. ET
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N SYM JENGRG NOTICE) DESCRIPTION DATE Tenx APPROVAL
2 A RELEASE Titel Paton€ B RELEASE Tufes|
>Nxe} ASCENT FAST LOOP
gE
A\55Al49a Aze7
Bin SIN”(RNac-RNes~ Neo)— BeOS A2is SIN AY =Nny Nze- nyNes- Nzo
1 V EVKEE HV AY =Sinay (14+ SINZAY_)Veve =|_| wt: WGOST A25\
I A2ZOs
VeryVytNyVyt Ve 4) TO ZEROVp=(VkX+Vy Y+Ve2)(R™) A2l6 >i ie A252Pre-nxX+ny V+ Z Sep =3-(w'\?7R Yo =By-AY GIMBAL ANGLE
SUBROUTINE4 =Bn"-Bm x105 (fat.SsDEFINED 4
A2I7 ¢ az30i =z = YWru = Yd Az58&7
x105 oe Wa) on ade ca .Te: Wiel-stu On= Oo >
Qr=QuWn™!Du = De -90)
Oe = Qu (i+ UST)" | feo! (0 +90) A253Gp =-5lAn +e) . Dei=DetS Du
GQsv dyihear) Baeon 2% AZ4S GEMINI Wre=VeLt+SWn Suey
: ==—Sy |+vaw(LEFT) SFA Orit+SOn (3 VOUTS/DEGREE)= + PITboaaay [mca ee esas
a Boe D%AQ, A; BY -Y, = FpSIN Agn = Ger Ar AREO+30° AD? =On2gn 3(5|N Aan\+(SIN gre) AG*O, Or,
J A244LIMIT ALTITUDE
ya2i9 = A232 ERROR SIGNALSINB= z¥2 AIG7 To “t-te KBs] $ TOF A256 LV2 Me eS 1A¥./ < 20 = Ddy= +(N248 +A) +ROLLCCWw)
B= Sina +58) IDSs} < 2O Aviv +(Na, AB + Nez AY)- Yd |+¥AW(LEFT)aay \" AG: +(Nes AS - Nag A¥)- Od |+ PITCHOOWN)
. a Q = Sas | :N-1 = Qn = Qe-Wa -1 = Ww Aer Qe? Os-KYye | A2s7
SIN - Ve ViLIMIT ALTITUDE
s PVr
T: SINT(I+SIN #T7/6)oweie
COMPUTE COSINE T A220 Avi s ce
| oe - es ee IAeuls GPAV=Ve-V+\, *Va Al53 Sra = Nee" PAB Ar Sit
; GUIDANCE A221 Srp =-AsVP*- SR cess= A\e *AV-a¢8Tu Kio = [C*T6*(Ge--5)]
Qu = AV(C'Y' Ke= Re-R+TeVe (Qg-!) aV/DEGREE)AQ=Qn-Qn-y Wor = Ke Kio A247 Ae__————t Ki =-Pa + Te Va(Qe-/) Rie
A249 acer rere, A208 Wyy = Ki Kio AVxb = Vga= Ag Sra se e 1 3 AVyb =Vop=Aq SrWa Wn-inll +AQ + 72 (AGE Ys (AQ)) ED oie
By = Va /AVe
Bn =Bgn +&+ To (Qe~1) Wer |A209 By = Br ~Te(Q-l) yy A235 Tomes A268
Ko SINT Eero <eDB * . 24 -
Vg? Vq- AU Ks A223 A270j EXIT
A210 Wee aw Ser (C*) oo ASCENT A269
P = (-\W*- Wg *Wer) FAST LOOP1.5- & AS,,= O= AY= O
7 ADv= O
A2i2 Aec4 ‘TO A260Vat =Vg - 1854E Ks
x105 2 2 xJ &Tu = (Vag + Vag) (Ag) - gere) 10Suw e+ Vac (Ae Bag (&
2ASCENT
Aal3
200-% + | A2ZZ25
: ms 1823*QeTo WeptSgr ty [Mea ((BEAEV2 ieee (oe Peete (oreirnine.ne. Artsinicarion'|| aasies Lael
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A3
A4
As =a 23/9 v2p
Ag = dva/aV
A7 = drg/OR-1
Ag = [ar av |8 al Pp
Ag = [ arp/av] “1a
C*
Cy
C5
Cpi, Cpo
Fy, Fy, Fz
Table E-1
SYMBOLS FOR MATH FLOW
A, ALPHABETIC (CAPITAL)
Stored constant usedto inhibit spacecraft yawangle computation.
Stored constant used to limit spacecraft allowableyaw angle.
Sensitivity coefficients used for SpacecraftInsertion Velocity Adjustment Evaluated atperigee,
Same as above only evaluated at apogee.
Effective exhaust velocity.
Initial eastward velocity at launch point due toearth rate,
Constant used to define orientation of spacecraftYp axis; with respect to east, while vehicle is onthe launch pad.
Constants defining step 1 and step 2 pitch rate ofthe launch vehicle.
Integrated acceleration components along platformaxes,
E-6
Table E-1. Symbols For Math Flow
Ky’, Kg', K3' Constants used in update of commanded platformgimbal angles after the platform is released butprior to liftoff.
Gravity component along vehicle. velocity vector.
Constants used to compute Stage 1 azimuth angleoffset to compensate for initial velocity and posi-tion perpendicularto the orbit plane.
Intermediate computer quantity used in calculatingpitch rate in steering.
Intermediate quantity used in gravity computation.
Commanded vehicle pitch rate.
Intermediate coefficients used in steeringequations.
Vehicie distance from earth center.
Desired insertion altitude.
Time read from TRS. Will remain zero until
lift-off.
Time to go. Used in Stage 2 steering equation.Defines time to effective thrust termination.
Time of update.
Total vehicle velocity.
Vehicle velocity perpendicular to the orbit plane.
Desired insertion velocity.
Velocity loss term approximating expected loss
due to gravity.
Velocity along the vehicle position vector
(Radial velocity).
E-7
Vy
Vet
VE
Vxqa, VG, VZG
Vxis Vyi» Vizi
Vxup, VYUP;VZUP
Vea
Vep
V'z
WN
X, Y, Z
Xo, Zo
Table E-1. Symbols For Math Flow (cont)
Velocity loss term approximating expected toss
due to steering (angle of attack).
Final value of gravitational velocity loss termremaining at shutdown.
Final value of steering velocity loss term re-
maining at shutdown.
Velocity update components transmitted from
ground,
Measured platform velocity components.
Platform velocity components interpolated to
update time,
Horizontal velocity increment required at perigeeto reach apogee.
Horizontal velocity increment required at apogee
to reach perigee.
Ground velocity update components corrected forazimuth orientation of platform.
Intermediate computer quantity used in vehicle
kinematic computations (W = e Vv /C ).
Vehicle position components.
Eastward velocity of earth resolved into platformframe.
B. ALPHABETIC (SMALL)
a4
a2
af
aT
Sine \, where is latitude of launch point.
Cosine \, where } is latitude of launch point.
Final value of thrust acceleration.
Thrust acceleration now.
Bl
@Tr
Sep
Bepi
8x, By» 87,
i
t
tp
tee
tR
tpi
tp2
Table E-1. Symbols For Math Flow (cont)
Value of thrust acceleration at nominal shutdown
time when W = 1.
Average value of thrust acceleration betweennominal and actual shutdown time.
Average thrust acceleration over previous computationcycle.
Gravity at vehicle altitude.
Effective gravity - gravity minus centripetalacceleration - along geocentric vertical.
Effective gravity at nominal shutdown condition.
Gravity components resolved along platform axis.
Inclination of Agena orbit plane.
Time after lift-off
Constant - time bias used to correct for delays in
receipt and detection of lift-off signal.
Constant approximately equivalent to the duration
of computer Stage 2 slow loop. Used in connection
with the initiation of SECO countdown.
Timeof autopilot gain change followinglift-off.
Constant used to compensate for any thrust
acceleration imparted to the vehicle following
the issuance of the shutdown discrete (mostly
cut-off impulse).
Time to start the roll program.
Time to stop the roll program.
Time to begin the step 1 pitch program.
Time to begin the step 2 pitch program.
At
Ats
GREEK (CAPITAL)
Table E-1. Symbols For Math Flow (cont)
Computer quantity used to delay entry intoinsertion velocity adjust program and to delayturn-off of the SECO discrete.
Time to start Stage 2 guidance. -
Intermediate quantity used in vehicle kinematiccomputations.
Thrust attitude required to compensate for vehicle |radial velocity.
Final value of commandedthrustattitude.
Computed value of vehicle pitch attitude. Actualvehicle pitch attitude with respect to localhorizontal.
Commandedvehicle yaw angle (with respect toorbit plane). Includes explicit yaw steering.
Vehicle yaw angle (with respect to orbit plane)required to kill velocity perpendicular to the orbit
plane.
Thrust attitude required to compensate foreffective gravity.
Final value of thrust attitude required for gravitycompensation.
Commanded vehicle thrust attitude with respectto local horizontal.
Vehicleflight path angle with respect to localhorizontal.
Length of slow loop computation cycle.
Accumulated time following entry into "SECOcountdown" loops. Also used to correct initial
computation cycle time following detection oflift-off.
E-10
Table E-1. Symbols For Math Flow (cont)
ATR
At'
AV
AVE
AY
6,¢,¥
Aaa¢Lv4¥ LV
ABvo:A¢ LVO:
AV vo
A856,445¢,4¥g¢
ABco?
AY sco
Ady
SCO’
8
6, Pp, Vp
On, ox» Yn
Time vehicle will roll at a constant rate to reachthe proper azimuth orientation.
Fast-loop cycle time (50 msec).
Total velocity to be gained prior to nominalshutdown including approximated velocity lossdue to gravity and steering.
Velocity to be gained corrected for actualshutdown time cutoff
(Ve= fi a)
Computed value of vehicle yaw attitude. Anglebetween vehicle X-axis and orbit plane.
Refer to pitch, roll, and yaw, respectively.
Computed vehicle attitude errors.
Limited vehicle attitude errors delivered toautopilot.
Computed spacecraft attitude errors during
insertion velocity adjust.
Limited vehicle attitude errors displayed to the
astronaut during insertion velocity adjust.
Vehicle roll offset required to compensate for
vehicle position and velocity perpendicular to the
orbit plane.
Vehicle pitch attitude error quantity.
Measured gimbal angles.
Commandedplatform gimbal angles during Stage 1.
During Stage 2, 9, andy are equated to actual
platform gimbal angles once per slow loop.
E-11
Table E-1. Symbols For Math Flow (cont)
Srp PPL VEL
Oy Pye MyPy
x
D. GREEK (SMALL)
Yo
Fast-loop commanded gimbal angles. , Thisincludes the effects of the pitch rate (P) term.
Commanded gimbalrates,
Coefficient used in computation of steering loss.
Average value of steering loss coefficient betweennow and shutdown.
Final value of steering loss coefficient at time ofshutdown,
Longitude of vehicle with respect to Greenwich.
Vehicle yaw attitude error quantity.
Longitude of ascending node of Agena orbit.
Rate of earth rotation.
Prior to platform release, angle between east andthe platform X-axis. The platform is torqued sothat its X-axis is parallel to the orbit plane.
y is positive when X is displaced north.
Value of y at the time of platform release.
Represents the angle between the launch site andthe orbit plane; positive when vehicle is beloworbit plane.
Spacecraft yaw angle requiredto kill velocity |perpendicular to the orbit plane.
Quantity used to allow convergence of certainStage 1 computations upon initiation of Stage 2guidance.
Position increment above or below nominal insertion.
altitude.
E-12
St
ST,
3V
8ra
érp
80, 8by, BV
Iy, Wy, 7
wt
w*
wPr
Table E-1. Symbols For Math Flow (cont)
Computed quantity which is used in the linear
interpolation of velocity data. Velocity data is
corrected to update time.
Computed quantity representing the adjustment
to nominal Stage 1 engine shutdown time.
Velocity increment above or below nominal
insertion velocity.
Total computed position increment above or
below apogee.
Total computed position increment above or below
perigee.
Fast-loop gimbal angle increments used to produce
desired pitch rate.
Matrix coefficients used to obtain platform com-
ponents perpendicularto the orbit plane.
Nodal precession rate of the orbit plane.
Pitch rate term used to keep thrust attitude con-
stant with respect to local vertical.
Pitch rate term used to satisfy vehicle altitude
constraint.
Pitch rate term used to compensate for apparent
rotation of gravity vector.
E-13
B. PLATFORM RELEASE TO LAUNCH
Following platform release, the computer will commence with the navi-gation function (A133, A134, A135 and A136). In addition, the computerwillupdate platform gimbal angles, which are changing due to earth rotation priorto launch (A118). The launch vehicle attitude errors (A256) will be computedduring this time as well as prior to platform release. These quantities, ifmonitored, could serve to provide some information on the operational readi-ness of the IGS system.
In block A106 the computer will be continuously reading the output of thespacecraft time reference system (Tg). Any change in this value from zerowill indicate that lift-off has occurred. The computer will then go into a fast-loop (A120, A121 and A122) to obtain the time of lift-off within approximately10 msec.
C. STAGE 1 — OPEN-LOOP STEERING
The magnitude of the roll maneuver (including offset for vehicle positionand velocity perpendicular to the orbit plane) is computed (A125) following lift-off. This angle in combination with tgp will be used to compute the time tostart a constant rate (1.25 deg./sec) roll program (tg), which will bring the ve-hicle to the required azimuth.
The vehicle will rise vertically and the computer will test (approximatelyevery 0.5 sec) for time to start the roll program (A156). At the proper time,gimbal angles and rates will be defined in block A161 andattitude errors forthe launch vehicle will be generated in block A256. Following the completionof the constant roll program, the commanded roll gimbal angle ($j) will beset equal to the value computedfor the final roll gimbal angle (¢ - A162).
The start of the first- and second-step pitch maneuvers will be con-
trolled by blocks A158 and A159. The time to provide the output for the gainchange discrete will be controlled by A164. The pitch profile produced is suchas to approximate a gravity turn, thus minimizing the angle of attack and,therefore, the normal forces on the vehicle. During Stage 1 as well as Stage 2operation, the platform gimbal rates will be computed in block A168 so asto producethe pitch rate desired. The open-loop pitch profile will be continuedthrough the staging interval and will be concluded upon computation of the firstStage 2 steering commands (A223 and A229).
D. STAGE 2 -- CLOSED-LOOP STEERING
Block A155 will control the time to initiate the Stage 2 steering computa-tions. Two passesare used to initialize Wy (A208) in Stage 2. During thistime, the open-loop pitch maneuver is continued for approximately 1 sec. Onthe third entry into the Stage 2 equations, the commandedattitudes and ratesobtained from the explicit steering equations are computed.
E-14
The equations as programmed will steer the vehicle into a plane, de-fined by the ephemeris data, to the height desired for insertion and will orientthe velocity vector so as to achieve the desired orbit. When the desired mag-nitude of velocity is reached, an engine shutdown command (A234) will begiven. This function is discussed in detail in the following paragraphs.
The vehicle velocity perpendicular to the orbit plane (V,), the velocityalong the vehicle radius vector from the center of the earth (Vp), and the ve-hicle position perpendicular to the orbit plane (P;) will be computed in blockA203. These quantities will be used in A221 and A222 to compute the vehiclecommanded angles and rates. Actual pitch attitude of the vehicle with respectto its local horizontal (Ay) and actual yaw attitude with respect to the orbitplane (AY) will be computed in A227. The quantities will be used in A229 todeterminethe pitch (94) and yaw (Q) attitude errors of the vehicle. @% andWo are then inserted into A256 where the fast-loop attitude errors are gen-erated. The desired vehicle pitch rate (P-Block A223) is used in A168 to ob-tain the desired gimbal rates which, in turn, are also used in the fast-loop at-titude error equations. (P, as computed above, does not include any excess
rate which might be required to bring the vehicle to the commandedpitch at-titude.)
Time-to-go (Tq) is continuously tested in A232. When this quantityisreduced to approximately 2 sec.,the attitude errors (A236) will be set to zero(thus allowing the vehicle rates to go to zero) and a fast countdown on SECOwill begin. At the proper time (A232), a SECO signal (A234) will be delivered.
E. ORBIT VELOCITY ADJUST
The ascent equations provide a capability to refine the spacecraft veloc-ity to meet the insertion conditions. The equations do this by using space-craft energy. The capability is required for the following reasons:
1. The guidance system may not satisfy these insertion con-ditions accurately.
2. Uncertainties associated with residual thrust of the ve-
hicle may exist following insertion.
3. The payload capability of the booster mayfall short ofthe energy required to meet insertion.
When the payload capability of the booster falls short of the insertion
conditions, a test is provided on AQ (A205). This test allows entry into the
orbit velocity adjust equations even when a SECOsignal is not delivered.
E-15
The perturbations from nominal insertion conditions (VL, Vp, bv» and5R) are computed continuously and form the basic inputs for the orbit velocityadjust equations. Approximately 20 sec. (A249 , A281) is allowed to elapse be-fore any commandsare generated for spacecraft thrusting. This elapse allowsthe zero attitude error signals (A236) to remain available for the launch ve-hicle during thrust decay; it also allows the astronaut time to separate thespacecraft from the launch vehicle.
Following this time, the commandedplatform roll gimbal angle will beset to approximately zero, and the spacecraft attitude errors will be computed,The astronaut will first roll the vehicle approximately 90 deg. to null the rollerror. This will be done in responseto the roll attitude error display in thecapsule. He will then null the yaw andpitch error appearing on the same dis-play.
The horizontal velocity will then be computed. This velocity will beeither added to or subtracted from the spacecraft at perigee to reach apogeeand at apogee to reach perigee. These quantities will appear on the AV me-ters in the spacecraft. While nulling out the attitude errors, the astronautwill then thrust the vehicle to either add or subtract the velocity appearing onthe AV indicators. As the spacecraft approaches the desired apogee (A246)the velocity to be added or subtracted at perigee will go to zero. When thiscondition is reached, thrusting is discontinued.
3
The velocity to be added or subtracted at apogee will be recorded by theastronaut. At this point, ascent guidance is essentially concluded. Theastronaut will use the "Catch-Up" mode of the computer to obtain the velocityincrement desired at apogee.
F. PLATFORM UPDATES
The computer has the capability of accepting velocity data from theground to correct for platform misalignment, and integrated errors in theplatform (A127, A128, A129 and A138 through A147). The use of velocitydata in correcting the azimuth orientation of the platform is discussed in Sec-tion II-B of this appendix.
The early updates in flight (t < 240 sec) will be used to correct the azi-
muth alignment of the platform; the updates following this time will be used tocorrect the measured platform velocities.
G. SWITCHOVER FADE-IN
One additional feature,which is not shown on the math flow but isscheduled to be inserted into the computer, is the set of equations used tofade in the attitude error signals when switchover occursfrom the primary
system to the IGS. These equations will have the effect of fading in the atti-tude errors when a slow drift malfunction occurs. They will also allow themajor percentage of the attitude error signal to be delivered to the autopilotwhen a rapid malfunction occurs. The result is to allow maximum controland response during rapid malfunctions and limited response during slowdrift malfunctions.
I. DERIVATIONS
A. RELATIONSHIP BETWEEN ANGULAR RATES OF GIMBALS,
SPACECRAFT AND LAUNCH VEHICLE
Vehicle
This diagram showsthe relation-
ship between the launch vehicle andspacecraft reference axes.
The symbols are defined as follows:
Target Pb = rotation about body xgxis - spacecraft roll, positive
as indicated
Qb = rotation about body yaxis - spacecraft pitch
rotation about body zaxis - spacecraft yawlb
vehicle rollPm
dm = vehicle pitch
Ym = vehicle yaw
The following relationships exist:
Pb = Pm “xb = “xm
Gb = lm Yb = Wem
Th = ~Im Yb = ~Yym
E-17
The autopilot command signals are documented as follows: To causethe launch vehicle to rotate in a positive direction (+ roll, + pitch, and + yawas defined above), the d-c voltage signal to the autopilot must be negative.The derivation of the relationship between gimbal rates and bodyrates isequivalent to the development of Euler's kinematical equations with specificapplication to the GEMINI gimbal system.
It can be shown that
Wb = @ sin V+ ?,
8 cos $¢ cos ¥ + Wsing,Yb =
and
Wh = - cos y sing +¥cos ¢.
Also,
Wy = 8 sin y+ ¢,
Wy = @ cos p sing - Wcos¢,
and
We = 6 cos ¢ cosy +psing.
Multiplying by r, we have
APm= A@siny + Ad,
Adm = APcosy sing - Ay cos¢,
and
Ary = A8cos¢ cosy + Aysind.
APm = Launchvehicle roll changein time t,
Aqm = Launch vehicle pitch change in time T,
and
Ary, = Launch vehicle yaw change in time r.
E-18
A@ = Change in @ intimer,
Aw = Change iny in timer,
and
Ad = Change ing in time r.
To implement a change in gimbal angle, the following notation will beassigned to present and desired gimbal angles:
6, Yp, Pp = present gimbal angles
8x, Yn, $n = desired gimbal angles
Now AG = Oy - 9p,
Ay = ¥y -¥p,
and
Ap = Fy - Pp.
As previously mentioned, a negative polarity is required to cause apositivé vehicle rotation. Therefore, Apm, Aq, and Arm mustbe multi-plied by -1 before being converted to analog signals. This can be accom-plished by the following operations:
46, =8y- on
Ave = Vp - Vy
Ade = bp - on
Subscript c denotes commanded change.
When a specific body angular rate is desired such as a pitch only maneu-ver during Stage 1, the following relationships are required:
tw, = Ag+A@ siny
Twy = A@ cosy sind - AW cos¢
tw, = A@ cos¢ cosh + Ap sing
E-19
or
sing cosA8@ = tw + TW, £08
cos y cos p
Ay = tw, singé - Tw, cos¢
sing siny cos@ sinyAd = Ty, - ww TH ——_—_—__—_—_
cos cos y
Setting
Wy = w =0, and Wy = P, we have
- « sing@ = ’
cos
Y = -Pcos¢,
and
p = - @sin y.
B. UPDATE OF COMPUTED ANGLES AND VELOCITY
Consider a platform which has been erected to the vertical precisely,
but is misaligned by an angle Ax about the platform Y axis.
IzIZ Ix, ly, 1z = Desired platform orientation.
Ix IXp, l¥p, 1Zp = Actual platform frame.
Ixp An = Misalignment in azimuth,positive
rotation about platform Y axisAn
ly, ly, Assumethat the ground tracking device can perfectly measure velocity
und transform the velocity into the desired platform frame. This frame is
known explicity.
E-20
Nowt
Vx = Vox + f x dt,t o
VY = fay dt,o
and
tVz = Voz + fag dt.
0
Vx, Vy, and Vz = actual velocities in desired frame as wellas measured velocities by ground station.
Vox and Voy = calculated velocity due to earth's rotationin the desired frame.
With a misoriented platform,t t
Vxp = Vox + fax cos An dt - faz sin An dt,t Oo 0
Vyp = fay at,0
andt t
Vzp = Voz + f az, cos An dt + fax sin An dt.o o
Here, Voy and Voz are values inserted during initialization.
If Ay is small and constant,
cos An = 1,
sin An =An,
and
J JVgp = Von + azdt + An ax dt.Zp Zo g O
Nowt
Vzp - Vz= An fax dt = An (Vx - Vox);Oo
or
VZp - VzAn =
Vx - Voy
E-21
It is now possible to establish the relationship between measurementsin the desired and actual frames.
IxXp 1 0 =-An [Ix
Iyp| = |0 1 0 IIy
IzZp An 0 1 In
This matrix must be used to transform ground velocities into the platformframe.
Vxp' = Vx- 4Vz
Vyp = Vy
Vzp'' = An Vx+Vz
Future updates now require that the primed values denoting groundmeasured velocity be transformed to calculated platform axes. Since ?y isoriginally assumed equal to zero, the following relationships are valid forthe general case of angle update:
V'Zp = Ny Vx + Vz
VZp - VZ'pAn = a
VXp - Vox
"xi = "Xi-1 + AqThe effect of platform misalignment on initial calculated velocity errors
(Voy and Voz) will now be investigated.
Initial velocity - Co Iz
Voy = Co cosyxX
Voz, = Cp sin y
Voxp = Co cos (y -An)
Vozp = -Co sin (y -An)
Ty
An IXp
Ip
E-22
By expanding and making small angle approximations, we have
Voxp = Cocos y+CosinyAn = Vox - Voz An,
and
Vozp = Co sin y + Cocos yAn = Voz +Voy Sn .
Vxp and VZp, however, must be updated to reflect the error in initial values.Therefore,
VXpp = VXp - Voz 49,
VZpe = VzZpt+ Vox An.
Positions X and Z must also be updated. So,
| Xo = X - Voz An T,
and
Ze Z+Voy An T
T is the elapsed time from platform release until update.
C. COMPUTATION OF VEHICLE AZIMUTH ANDPITCH ANGLE ORIENTATION
During Stage 2 flight, the actual vehicle attitude is required to imple-ment the steering commands. The required angles are shown in Figure E-2.
Rp=1, X + I, Y + Iz Z defines the vehicle position in theplatform frame
The X-axis of the launch vehicle can be defined with respect to theplatform by using the following standard GEMINI platform-to-body relation-ships:
Ixp Ixbij
Typ = Platform to ly- BodyIZb IZ
Exp = Fx 08 ¥p 08 Op - Ty cos Wp sin Oy - Tz sin py
E-23
Also
Rp Ix, = WR cos@ = RsinBy ,
andxX Y Z
sinB Mm = —- cos fp cos 9, - — cosp sin@, - — sinvpR R R
Similarily, a unit vector perpendicular to the orbit plane has been defined in
terms of the platform axis:
Ty = x Ix + Ny ly +77 1y
By using a similar equation,
sin AY = 7, cos Wp cos Gy - Ny cos Wp sin 6, - Nz sin Vp
SS JVECTOR NORMAL TO ORBIT PLANE
PLANE DEFINED BYNORMAL TO ORBITPLANE AND VEHICLEX=AXIS
PLANE DEFINEO BYPOSITION VECTOR ANDVEHICLE X-AXIS
ORBIT PLANE
LOCAL HORIZONTAL
POSITION VECTORWHICH DEFINESLOCAL HORIZONTAL
Bu is the actual pitchattitude of the vehicle
with respect tothe localhorizontal.
AY is the azimuth anglewith respect to the or-
bit plane.
Figure E-2. Vehicle Azimuth and Pitch Angle Orientation
E-24
D. SUMMARY
The guidance equation portion of the simulation consists of the follow-ing subroutines: (1) DI (discrete inputs, (2) FAST (IGS fast-loop attitude errorcomputations), (3) GUID 1 (Stage 1 open-loop guidance equations) and (4)GUID 2 (Stage 2 closed-loop guidance equations). Fortran listings of theseprogramsare included in Table E-II.
1. Differences Between Math Flow and Equations Used in Simulation
To date, simulation effort has been primarily devoted to the verifica-tion of the compatibility of the IGS equations and the vehicle model. Thefol-lowing portions of the IGS math flow remain to be programmed and/or exer-cised:
e Test for Lift-off
e Gimbal Angle Update Following Platform Release
e Launch Azimuth Offset
e Platform Velocity Update
° Orbit Velocity Adjust
e Stage 2 SECO
All of the above items will be incorporated into the simulation prior to
the final simulation report.
2. Operation of IGS Guidance Simulation (See Figures II-1 and D-2)
The guidance equations accept ephemeris data from the main program.
Guid 1 then updates this data while waiting on platform release. Upon re-
lease, Guid 1 begins navigation; inputs to the navigation equations (the measured
accelerations) are calculated by the main environment. After a nominal
elapsed time increment, lift-off is simulated and fast-loop attitude error com-
putations are begun. The fast loop accepts the gimbal angles from the main
environment which is keeping track of vehicle inertial attitude. Commanded
gimbal angles are generated in either Guid1 or Guid 2. The attitude errors
generated in the fast loop are then used asinputsto the simulated autopilot
and vehicle model which, in turn, send vehicle angular rates back to the main
program. The main program usestheserates to update the vehicle gimbal
angles. Subsequently, another fast loop computation cycle may be performed.
With the exception of a few discretes, no other data need be transferred
between the environment and IGS equations.
The fundamental computation cycle time used in the simulation of the
Guid 1 as well as Guid 1 and 2 equations is 0.5 sec. This increment may be-
comeslightly smaller for the Guid 1 operations and slightly larger for the
Guid 1 and 2 operations when the computation cycle time of the IGS equations
as programmed in the GEMINI computer is defined more accurately.
E-25
A.
Table E-2
SYMBOLS USED IN ASCENT
GUIDANCE SIMULATION(Stage 2)
CONSTANTS
Env.
Symbol Fortran
Symbol
A3 52K ( 1)
A4 52K ( 2)
A5 52K (3)
A6 52K ( 4)
AT 52K ( 5)
A8 52K ( 6)
AQ 52K ( 7)
Wy 52K ( 8)
QN 52C ( 1)
Vp 52C ( 2)
VY» 52C ( 3)
Vg 52C ( 4)
a 52C ( 5)
Env.
Symbol FortranSymbol
c* 52C ( 6)
KQ 52C ( 7)
Va 52C ( 8)
TE 52C ( 9)
V\F 52C (10)
2K 52C (11)4
«12 52C (12)l
tee 52C (13)
Re 52C (14)
tk 52C (15)
ts1 52C (16)
Gepf 52C (17) E-26
B. VARIABLES
Table E-2. Symbols Used In ©Ascent Guidance Simulation (Stage 2) (cont)
Env. *Symbol Fortran From
Symbol
t TIME E
6B THEB E
VB PSIB E
N20 A20 1
Be p DELEP 2
Sey DELEY 2
Adiy ER 2
AGy EP 2
AY Lv EY 2
Vx VP (1) 1
Vy VP (2) 1
Vz VP (3). 1
x RP (1) 1
y RP (2) 1
Zz RP (3) 1
Ny ETX 1
*E - Environment1 - 1St Stage Guidance2 - 2nd Stage GuidanceK - Constant
_ Env. *
Symbol Fortran FromSymbol
Ny ETY 1
Nz ETZ 1
g GT 1
N25 A25 1
N26 A25 1
Lig DTS 2
LC29 LC29 2
Atseco — 2
p Pi 2pf PHIF 1
LCA232 LCA232 2
R RM 1
8) — _—
PS52D PS2D K
LC24 — _
E-27
9
Cc
AAMAaADa
Cc
80B COFERJAN. 91963SUBROUTINE GUID]DIMENSION VP0(3)_VP1(3) 4F (3) .6(3),RP(3)VG(3),0VP(3),V1(3),0V5(3) eOVIC124) sFPO(3) s0V6( 24) »RRP(3)®ROFE(3)COMMON DV1,011,012,013,
XINCL »DFL,OT sOMEGAE y OMEGAP ,CO4C5yY0,TRE eTRe TP 1, TP2,TGCyCP1yCP2,C 1 eC2,GIP FP,VG,
THEB, PSIB,PHIB, THEFL, PSI FL »PHIFL sOTHEN,DPSINA205A21,A22,A23,A24
1 OV6eVPeRPVETXsETY GETZ ¥GT9A259 A265 DTS LC29yPHINRM,OEL 1,MS20,LC24,0TSFORMAT (6618.8)IF (LCV) 114,113,113
1913 RRP(2) = -.209097N9E8RP(2) = —.209097K9E8
SINT = SINF(XINCL)7 COSI = COSFIXINCL)
tas
119W17iW145116
11812TI
7273By
LCI = -2N= Nt ]IF (LCA232) 118,119,119IF (LC29) 112,117,197IF (N — 91) 111,112,112TF (O82) 116,115,115CALL DICALL FASTRETURN
DT = OTSN= 0T=T +01If (L018) 73,72,72Tz=0.
IF (LC29) 51,8%,84%DFL = OFL + DOT * (OMEGAE - OMEGAP)Bl = SINF(OFL)
B2 = COSFI(DFL)SGM = +SINI #82GM = SGM#(1. ~- SGM#SGM/6.)IF (£026) 13,111,171IF (DI3 913,32,12SDL = -Al*#COSI + A2#SINI«#B]
CGM = 1.-SGM#SGM/2.
E-28
0 VP (3) 4X(3)5V(3) sVUP(3),
TUsA1,A2,GK,TBECO,DV5»,JUP,F,
sPlePHIF »LCA232,
3
31
18
152
16161
7
71
21
22
23
vPO(1)= CO*#CGMvP0(3)=-C0#SGMve (1) = vPotl)yvP(3) = vP0(3)ETY = SOL
ETZ = 1.
PHIN = C5 - GM
THEN = 1.5707963PHINI = 0.
THENY = 0.PSINIT = 0.PHIFL = PHIN
THEFL = THEN
PSIFL = PSIN
PHIB = PHINTHEB = THENPSIB = PSINGO TO 53
R2 RPC 1) #82 + RP(Z)ee2 + RPC Z)#H2
RM SQRTF(R2)GT =GK/R2XKG = GT/RMDO 18 I = 193GCI) = XKG #RP(T1)VPI(I) = VPC(T)FSTORE = F(2)F(2) = ~F(3)F(3) = FSTORE
Hott
DO 16 I =193VP(I) = VPCI) + FCT) -— GCT)#DT
FPO(I) = FUT)F(I) = 0
00 17 I = 123ROFECI)=ROFE( IT) 4(VPC(I) + VPI(I))#QT/2.
RP(1) =RRPCI) + ROFE(T)
QT = DTIF (LC21) 25519419
IF (TU - T) 23,2121
Tl=TDO 22 1 = 193VICI) = vel)GO TO 31DELT = (Tv -— T1)/0TpO 24 I = 193
E-29
24
25
26
28
2931
32
36
3A1
38
VUPCTI) = VECI) © OELTa(vPCT)- VICID)TU = TU + 50.
GO TO 31
LC21 = 2
IF (308.-— TU) 28,26226
ZOS = VUP(1)#ETX + VUP(2)#ETY + VUP(3)eETZ
OPSI =(VG(3) ~ ZOS)/VUP(1)
DVP(1)= ¢OPSIT#VP0(3)DVP(3)= ~DPSITevPO(1)
VP(1) = VP(1) + DVP(?)
vP(3) = vP(3) + DVP(3)
RP(1) = RPC?) + OVP(1)
RP(3) = RP(3) + DVP(3)
ETX = ETX ~ OPSI#ETZ
ETZ = ETZ + DPSI#ETX
GO TO 31
TU = TU ~ 4O.
pO 29 I = 1,3
VP(I) = VPCI) + VGCI) — VUP(T)Zl = SEINF(PHIB)
Z2 = COSFIPHIB)
Zu = COSF(PSIB)
A20 SINF(PSIB)
A21 Zu oe 22
A22 zt
A23 Zhe 21
A24% z2
A25 Zu eSINFC(THEB)
A26 = 24 sCOSFUTHEB)
If (£CA232) 322,323,323LCA232 = 2
RETURN
IF (TBECO — 1) 52,33,33IF (CC18) 36,345,348
IF (O12 ) 35,53,53tc 8 = —2e
TR = TRE — 45.83662b8(C5 -GM ~1.5707963 *#CleSOtL + C2#COL}
PHIF = PHIN — CTRF -— TR) #.023816615
PHIFL = PHIN
THEFL = THEN
PSIFL = PSIN
IF CTR — FT) 37,49,n9
If (TYRE - T) 39,38, 38
PHINE =-.0218 16616
i
E-30
ams
53
hO
909192
39|
4243
4,45H648
49
51
52
PHIN = PHIN + PHINT#OTGO TO 49IF (TPL -T) 82,41,41PHIN = PHIFPHIN? = 0.GO TO 49TF (TP2 -T) 44,433Pl = CPIGO TO 48IF (TGC -— T) 45,4%6,46DOS7 = -2Pl = CP2PSINT =-PT#COSF(PHIN)THEN) = PI#SINF(PHIN) /COSF(PSIN)PHINT =-THENIT#SINF(PSIN)PHIN = PHIN + PHINT#OTTHEN = THEN + THENT#OTPSIN = PSIN + PSIN1#DTDPSIN PSIN1I#D1T/10.DTHEN THEN} *#DT/10.OPHIN PHINT#DT/ 10.GO TO 53CALL GUID2RETURNCALL GUID2GO TO 48
GO TO 114ENO
WADDING 6059 GEMINI ASCENT GUIDANCE 4&8
JAN, 91963
6059 GEMINI ASCENT GUIDANCE-2ND STAGE OICK WADDING
SUBROUTINE GUID2
DIMENSION 01(24),02(5),03049),D4(6) ,05(4&) ,O06(2) ,D7(17) ,DIA(25),
C 03A(31)
COMMON Dt,TeDIA,
Cc Nay AU yASAb AT ABs ADs WNe D23QNe VF oe VL eo VGeAFByCSyCKy VA,TEDV
LF ,CU2,C112, TCC RE, TK,TS1,GEPF,D3,TAU,D3IA,
C TB»PBsPHBsDEyEN2Z0eD5yTP0ePP0, 0G20PLYV
ZO,DTLVOyDSLVOsD ly X] eV eZi aXe VoZ gEXvETY pETZyC3eEN2Z5,ENZ6,DTSyLC29,
BPHN »Pl,yPF,LCA232,R,D0EL 1lyMS2D0,DTC2
IF (1029) 500,40,40
VN2=X lee 2+Y Lew24+Z #82LCA232=1
VN=SQRTF(VN2)
VYP=VY
VPP=VvP
VY=—-XT#ETX4+YI*ETY+Z1
VP=(XaxT4+VaVYI+Z"eZ1)/R
RIS~-ETX#X#ETY#Y+Z
HI=R1
IF (LCO24) 90,99,99
IF (TSO-T) 92,91,91
RETURN
DO064=)
DELV=VF-VN
DELR=RF-R
IF (DELV-A3) 94,93,93
"Wd
E-31
100101
1010
102
103
10%
12
3Wu
10
OVE=DV-AFB#DTUQNP=QNQN=DV/CSDQ=QN-QNPIF (ABSF(0Q)-CK) 100,100,103IF (ABSF(VF-VNI-VA) 102,101,101SENSE LIGHT 4&WRITE OUTPUT TAPE 9,1010FORMAT (20H ERROR AT BLOCK A206)RETURNLC2u=-1GO TO 521WNP=WNWN=WNP#(3.40Q#( 1.+0Qe(.5+1./6280Q)))Ch=C3*SGMVG=VG-TAUHChIF (DEL1-1.5) 104,104,172DELT=OEL 1+1.GO TO 200
’ VGF=VG—(TE-TAU)/2.4CHOTU=(VGF4VLF)/AFB
DEL3=T-Ch2
IF (DEL3) 14,133,173VLF=VL-BLM#DVE
WS2=VN2 eCGM#e2/Rea2WS=VN#CGM/R
GEP=C3-WS2#RUl=(WNP-WN) /TAUAU=U1#8CSTE=(WN-1.)/U1-DTU
AT=AU/WN
AF=AU/(1.4U1T#0TU)
AFB=.5#( AU+AF)
ATT=AT#(1.-U1/2-8TAU/WN)
SBG=GEP/AT
BGNP=BGN
BGN=SBGe(1.+SBG##2/6.)
SBB=—VP/DVEBB=SBB#(1.+SBBe#2/6.)
DELY=VY/DELVIF CABSF(DELY)-AS) 98,95,95IF (DELY) 96,97,97DELY=-A4uGO TO 1800DELY=A4GO TO 1800VIs1./VNS$G=VP#VICG2=1.-SGe#2CG=.5#CG2+.5GM=SG#(1.+SG"#2/6.)SGM=SGCGM=CGOV=VF~-VN+VL4VG
E-32
We
5
16
161
1800
170
501
500
5152521
520
53
71
Q5=1.-DVE/AF/TEQ6=Q5/DVEeCSIF (T-C112) 15515516C6=RF-R-TE#VP#( 1.-Q6)WPR=C6/CS/TE##2/ (06-25)
WYY=(-RT4TE#( Q6-1. 2) #VY) /(CSeTEea2e(Q6—-.5))
WG=2.8#WS+GEP/CS
BYB=VY/DVE
SS=TE*#WPR#(Q6—-1.)
BNPP=BGN+4BB+4SS
BY=BY8-TE#(Q6-1.) #WYY
PI=WPR-WS-WGBGF=GEPF/AFB
BPP=BB+TE#Q6#WPR+BGFFLAM=.58#(BPPae2+BYee#2)XL=.58( (BNPP—-GM) ##24+(BY-VIeZ1) 42)
BLM =.5#(XL+FLAM)VL=VL-XL#TAUSATTBM=ARS INF (X/R*EN26—-Y/R#ENZ5~Z/R#EN2ZO)
SOT=ETX #EN26—-ET Y#EN2Z5~EN20
DT=SOT#(1.+SDT##2/6.)IF (LC24) 171,170,170
PPO=BY-DT
TPO=BNPP-BM
PFL=PB
TFL=TB
PN=PB
IN=TBPHFL=PHNIF (TE-TK-TCC) S50 502501
LCA232= 1GO TO 200DTS=DTS+.05DTC2=DTS-(TE-TK)IF (O0TC2) 52,53,53
LC29=-1TSO0=T#3.5TS 1=T+20.OTLVO=0.
DPLVO=0.
OSLV0=0.P1=0.
GO TO 200
poék=-1.LCA232=-1
LC29=1LC2k=-1GO TO 520IF (LONF) 173,172,172
E-33
72
1737h175176
177178179180181182
200201202
203
LC i=)
LC3=1Lc8=1LCNF=-1IF (LCV) 175,178,175
GO TO 200IF CFSI-T) 1762174, 174%PHN=PF-1.5708
DSSC=DT-DELYOTSC=B8M
OPSC=PHB=PHN
COc0=. 349066IF (ABSF(OSSC)J-COCO) 178,178,177
DSSC=SIGNF{COCO,0SSC)IF (ABSF(DTSC)-COCO) 180,180,179OTSC=SIGNF(COCO,07TSC)IF (ABSFI(DOPSC)-—COCO) 182,182,181
DPSC=SIGNF(COCO,OPSC)DRA=A5 #VPHe2+A6eDELVtATeDELRDRP=-A5 #VP##2~DELR
DVXB=A8 «DRAVGA=DVXB
DVYB=A9 #DRP
VGP=0VYBOVZ8=0.
IF (MS20) 201,202,202
RETURNWRITE OUTPUT TAPE 9,203,LCA232,LC29,LC2NU,LCI,LC3,LC8 gLCRF, VN, VY, VP
19R1,006%, DEL Vs DELR es DELY oGMy DVe DVEs QNe DQ a WNy Cg VG_ VGF,OTU,VLFWS GE
2PeULeAUs TEs ATs AF es AF Bs ATT, BGN ey BB 25 2p Q6 eC Oe WPReWYY eWG ep BYBe BNPP e BY »P I3,BGFyBPP,FLAM,XL,yBLM,VL ¢BMeSDT,DTgPPO,TPOePFL eo TFL ey PN, TN,yPHFL,DTS,D
YTC2,TSOeTS1I,O0TLVOeDPLVO »OSLVOsPHN,OSSC,DTSC,DPSC,DRA, DORP, VGA, VGP 4D
5VZBFORMAT (715/(8E15.7))CALL POUMP(D1(1),01(500), 1)RETURNENO
B-34
BOB COFERSUBROUTINE FAST
DIMENSTONOV1(125) .0V2(35)COMMON OV1,DI2,0V2,
C THEB,yPSIB,PHIB, THEFL,PSIFL »PHIFL »DTHEN, DPSIN, DPHIN,A20C 9A21,A22,A23,A24, DELEPs DELEYVs DEP, DEV, ER EP ,EY
IF (DI2) 3,4,4%3 PHIFL = PHIFL
PSIFL = PSIFL
THEFL = THEFL DTHENDELEP = OELEP DEPDELEY = DELEY + DEY
DPSI =~PSIFL + PSIBDPHI =-PHIFL + PHIB
DTHE =-THEFL + THEBER=+( A20#DTHE + DPHT)
EP=+((+A23*eDTHE ~ A2u#DPSI) - DELEP)EY=4+((A21#OTHE + A22*DPSI) - DELEY)
2 FORMAT (6618.8)
QQ =QQ +1.IF (QQ ” FP) 4,5,5
S WRITE OUTPUT TAPE 992, ERsEYeEP, PS1IB,PHIB, THEB
QQ = 0h RETURN
END
BOB COFERSUBROUTINE DIDIMENSION CT(3),0V1(118)COMMON DV1,CT, TESPR,yTFPRyDTIME sDI 1,012,013TA= TA+ OTIMETEPR = TA -TFSPRBF (CT(3) — 1A)3—398
3 O13 = -2.IF (LCV) 4,31,31
31 TFSPR = TA
DPHINDPSIN
+++
+
LCI = -2h IF (CTC1) — TA) 5,5,85 O11 = -2.6 IF (CT(2) — TA) 72787? O12 = -2.8 RETURN
END
E-35/36